![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > syld3an3 | GIF version |
Description: A syllogism inference. (Contributed by NM, 20-May-2007.) |
Ref | Expression |
---|---|
syld3an3.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
syld3an3.2 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
syld3an3 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 939 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑) | |
2 | simp2 940 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓) | |
3 | syld3an3.1 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
4 | syld3an3.2 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) | |
5 | 1, 2, 3, 4 | syl3anc 1170 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 920 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 922 |
This theorem is referenced by: syld3an1 1216 syld3an2 1217 brelrng 4624 moriotass 5575 nnncan1 7621 lediv1 8224 modqval 9620 modqvalr 9621 modqcl 9622 flqpmodeq 9623 modq0 9625 modqge0 9628 modqlt 9629 modqdiffl 9631 modqdifz 9632 modqvalp1 9639 expival 9794 bcval4 9995 dvdsmultr1 10614 dvdssub2 10618 divalglemeuneg 10703 ndvdsadd 10711 |
Copyright terms: Public domain | W3C validator |